Small molecules can regulate protein reactivity by binding to residues distant from the active site, a phenomenon known as allostery. Monod, Wyman, and Changeux (MWC) explained allostery in multi-subunit proteins with a widely-applied theoretical model in which binding of so-called allosteric effectors alters the equilibrium between more-reactive (R) and less-reactive (T) quaternary structures. In their model, each quaternary structure has a single reactivity. We use silica gels to trap unstable protein conformations and a new kind of laser-photolysis experiment to show that hemoglobin, the paradigm of allostery, exhibits fast and slow ligand binding phases with the same rates in both R and T quaternary structures. Allosteric effectors change the fraction of each phase but not the rates. These surprising results are readily explained by the simplest possible extension of the MWC model to include a pre-equilibrium between tertiary conformations that have the same functional properties within each quaternary structure.